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Research Article | Open Access

Endpoint Morrey interior regularity of stable solutions to the p-Laplace equation

Meng Qu1( ), Zhi Wang2
School of Mathematics and Big Data, Chaohu University, Hefei 238000, China
School of Mathematics and Statistics, Anhui Normal University, Wuhu 241002, China
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Abstract

This paper establishes interior Morrey regularity for stable solutions of the p-Laplace equation − Δ p u = h ( u ) in B 1 ⊂ R d , where h belongs to C 1 ( R ). The results cover the endpoint case left unresolved by Cabré et al. Moreover, for positive nonlinearities h, a global Morrey estimate was obtained for stable solutions of a Dirichlet problem on any smooth, bounded, strictly convex domain.

Keywords

stable solutionp-LaplacianMorrey spaceregularity

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Electronic Research Archive
Volume 34 Issue 7,
July 2026
Pages 4765-4776
DOI: 10.3934/era.2026210

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Cite this article:
Qu M, Wang Z. Endpoint Morrey interior regularity of stable solutions to the p-Laplace equation. Electronic Research Archive, 2026, 34(7): 4765-4776. https://doi.org/10.3934/era.2026210

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Received: 07 March 2026
Revised: 06 May 2026
Accepted: 21 May 2026
Published: 15 July 2026
©2026 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)